The objective of this paper is to present the results of a detailed uncertainty analysis for high-fidelity fluid-structure interaction modeling over a deformable Hypersonic Inflatable Aerodynamic Decelerator configuration at peak heating conditions for a ballistic Mars en- try. Uncertainty results are presented for the structural response (deflection) and surface conditions (pressure, convective heat transfer, and shear stress) of the deformable inflatable decelerator with an efficient polynomial chaos expansion approach with sparse approximation. Approximately half of the uncertain flowfield and structural modeling parameters showed significant contribution to the inflatable decelerator deflection and resulting surface uncertainties, subject to a number of epistemic and aleatory uncertainties associated with the structure and flowfield. Global nonlinear sensitivity analysis shows that the tensile stiffnesses of the inflatable torus structure, cords, and straps, and the inflation pressure are the main contributors to the uncertainty in the inflatable decelerator deflection. The freestream density and shape deformation significantly contribute to the uncertainty in the aerodynamic heating, wall pressure, and shear stress. The CO2-CO2 binary collision interaction is also shown to be a significant contributor to aerodynamic heating and shear stress uncertainty.